Latent multinomial models for extended batch-mark data.

Batch marking is common and useful for many capture-recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture-recapture models to such data requires one to identify all possible sets of capture-recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.

Understanding the impact of correlation within pair-bonds on Cormack-Jolly-Seber models.

The Cormack-Jolly-Seber (CJS) model and its extensions have been widely applied to the study of animal survival rates in open populations. The model assumes that individuals within the population of interest have independent fates. It is, however, highly unlikely that a pair of animals which have formed a long-term pairing have dissociated fates.We examine a model extension which allows animals who have formed a pair-bond to have correlated survival and recapture fates. Using the proposed extension to generate data, we conduct a simulation study exploring the impact that correlated fate data has on inference from the CJS model. We compute Monte Carlo estimates for the bias, range, and standard errors of the parameters of the CJS model for data with varying degrees of survival correlation between mates. Furthermore, we study the likelihood ratio test of sex effects within the CJS model by simulating densities of the deviance. Finally, we estimate the variance inflation factor c ^ for CJS models that incorporate sex-specific heterogeneity.Our study shows that correlated fates between mated animals may result in underestimated standard errors for parsimonious models, significantly deflated likelihood ratio test statistics, and underestimated values of c ^ for models taking sex-specific effects into account.Underestimated standard errors can result in lowered coverage of confidence intervals. Moreover, deflated test statistics will provide overly conservative test results. Finally, underestimated variance inflation factors can lead researchers to make incorrect conclusions about the level of extra-binomial variation present in their data.

Effects of snake fungal disease on short-term survival, behavior, and movement in free-ranging snakes.

Pathogenic fungi are increasingly associated with epidemics in wildlife populations. Snake fungal disease (SFD, also referred to as Ophidiomycosis) is an emerging threat to snakes, taxa that are elusive and difficult to sample. Thus, assessments of the effects of SFD on populations have rarely occurred. We used a field technique to enhance detection, Passive Integrated Transponder (PIT) telemetry, and a multi-state capture-mark-recapture model to assess SFD effects on short-term (within-season) survival, movement, and surface activity of two wild snake species, Regina septemvittata (Queensnake) and Nerodia sipedon (Common Watersnake). We were unable to detect an effect of disease state on short-term survival for either species. However, we estimated Bayesian posterior probabilities of >0.99 that R. septemvittata with SFD spent more time surface-active and were less likely to permanently emigrate from the study area. We also estimated probabilities of 0.98 and 0.87 that temporary immigration and temporary emigration rates, respectively, were lower in diseased R. septemvittata. We found evidence of elevated surface activity and lower temporary immigration rates in diseased N. sipedon, with estimated probabilities of 0.89, and found considerably less support for differences in permanent or temporary emigration rates. This study is the first to yield estimates for key demographic and behavioral parameters (survival, emigration, surface activity) of snakes in wild populations afflicted with SFD. Given the increase in surface activity of diseased snakes, future surveys of snake populations could benefit from exploring longer-term demographic consequences of SFD and recognize that disease prevalence in surface-active animals may exceed that of the population as a whole.

On continuous-time capture-recapture in closed populations.

Schofield et al. (2018, Biometrics 74, 626-635) presented simple and efficient algorithms for fitting continuous-time capture-recapture models based on Poisson processes. They also demonstrated by real examples that the standard method of discretizing continuous-time capture-recapture data and then fitting traditional discrete-time models may lead to information loss in population size estimation. In this article, we aim to clarify that key to the approach of Schofield et al. (2018) is the Poisson model assumed for the number of captures of each individual throughout the study, rather than the fact of data being collected in continuous time. We further show that the method of data discretization works equally well as the method of Schofield et al. (2018), provided that a Poisson model is applied instead of the traditional Bernoulli model to the number of captures for each individual on each sampling occasion.

Selectivity underlies the dissociation between seasonal prey availability and prey consumption in a generalist predator.

Generalist predators are capable of selective foraging, but are predicted to feed in close proportion to prey availability to maximize energetic intake especially when overall prey availability is low. By extension, they are also expected to feed in a more frequency-dependent manner during winter compared to the more favourable foraging conditions during spring, summer and fall seasons. For 18 months, we observed the foraging patterns of forest-dwelling wolf spiders from the genus Schizocosa (Araneae: Lycosidae) using PCR-based gut-content analysis and simultaneously monitored the activity densities of two common prey: springtails (Collembola) and flies (Diptera). Rates of prey detection within spider guts relative to rates of prey collected in traps were estimated using Roualdes' cst model and compared using various linear contrasts to make inferences pertaining to seasonal prey selectivity. Results indicated spiders foraged selectively over the course of the study, contrary to predictions derived from optimal foraging theory. Even during winter, with overall low prey densities, the relative rates of predation compared to available prey differed significantly over time and by prey group. Moreover, these spiders appeared to diversify their diets; the least abundant prey group was consistently overrepresented in the diet within a given season. We suggest that foraging in generalist predators is not necessarily restricted to frequency dependency during winter. In fact, foraging motives other than energy maximization, such as a more nutrient-focused strategy, may also be optimal for generalist predators during prey-scarce winters.

Connecting the latent multinomial.

Link et al. (2010, Biometrics 66, 178-185) define a general framework for analyzing capture-recapture data with potential misidentifications. In this framework, the observed vector of counts, y, is considered as a linear function of a vector of latent counts, x, such that y=Ax, with x assumed to follow a multinomial distribution conditional on the model parameters, θ. Bayesian methods are then applied by sampling from the joint posterior distribution of both x and θ. In particular, Link et al. (2010) propose a Metropolis-Hastings algorithm to sample from the full conditional distribution of x, where new proposals are generated by sequentially adding elements from a basis of the null space (kernel) of A. We consider this algorithm and show that using elements from a simple basis for the kernel of A may not produce an irreducible Markov chain. Instead, we require a Markov basis, as defined by Diaconis and Sturmfels (1998, The Annals of Statistics 26, 363-397). We illustrate the importance of Markov bases with three capture-recapture examples. We prove that a specific lattice basis is a Markov basis for a class of models including the original model considered by Link et al. (2010) and confirm that the specific basis used in their example with two sampling occasions is a Markov basis. The constructive nature of our proof provides an immediate method to obtain a Markov basis for any model in this class.

Individual quality and personality: bolder males are less fecund in the hermit crab Pagurus bernhardus.

One explanation for animal personality is that different behavioural types derive from different life-history strategies. Highly productive individuals, with high growth rates and high fecundity, are assumed to live life at a fast pace showing high levels of boldness and risk taking, compared with less productive individuals. Here, we investigate among-individual differences in mean boldness (the inverse of the latency to recover from a startling stimulus) and in the consistency of boldness, in male hermit crabs in relation to two aspects of life-history investment. We assessed aerobic scope by measuring the concentration of the respiratory pigment haemocyanin, and we assessed fecundity by measuring spermatophore size. First, we found that individuals investing in large spermatophores also had high concentrations of haemocyanin. Using doubly hierarchical-generalized linear models to analyse longitudinal data on startle responses, we show that hermit crabs vary both in their mean response durations and in the consistency of their behaviour. Individual consistency was unrelated to haemocyanin concentration or spermatophore size, but mean startle response duration increased with spermatophore size. Thus, counter to expectations, it was the most risk-averse individuals, rather than the boldest and most risk prone, that were the most productive. We suggest that similar patterns should be present in other species, if the most productive individuals avoid risky behaviour.

Mark-recapture with multiple, non-invasive marks.

SUMMARY: Non-invasive marks, including pigmentation patterns, acquired scars, and genetic markers, are often used to identify individuals in mark-recapture experiments. If animals in a population can be identified from multiple, non-invasive marks then some individuals may be counted twice in the observed data. Analyzing the observed histories without accounting for these errors will provide incorrect inference about the population dynamics. Previous approaches to this problem include modeling data from only one mark and combining estimators obtained from each mark separately assuming that they are independent. Motivated by the analysis of data from the ECOCEAN online whale shark (Rhincodon typus) catalog, we describe a Bayesian method to analyze data from multiple, non-invasive marks that is based on the latent-multinomial model of Link et al. (2010, Biometrics 66, 178-185). Further to this, we describe a simplification of the Markov chain Monte Carlo algorithm of Link et al. (2010, Biometrics 66, 178-185) that leads to more efficient computation. We present results from the analysis of the ECOCEAN whale shark data and from simulation studies comparing our method with the previous approaches.

Smoothing population size estimates for time-stratified mark-recapture experiments using Bayesian P-splines.

Petersen-type mark-recapture experiments are often used to estimate the number of fish or other animals in a population moving along a set migration route. A first sample of individuals is captured at one location, marked, and returned to the population. A second sample is then captured farther along the route, and inferences are derived from the numbers of marked and unmarked fish found in this second sample. Data from such experiments are often stratified by time (day or week) to allow for possible changes in the capture probabilities, and previous methods of analysis fail to take advantage of the temporal relationships in the stratified data. We present a Bayesian, semiparametric method that explicitly models the expected number of fish in each stratum as a smooth function of time. Results from the analysis of historical data from the migration of young Atlantic salmon (Salmo salar) along the Conne River, Newfoundland, and from a simulation study indicate that the new method provides more precise estimates of the population size and more accurate estimates of uncertainty than the currently available methods.

Continuous covariates in mark-recapture-recovery analysis: a comparison of methods.

Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark-recapture-recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data-generating mechanism.

High prevalence of smoking among urban-dwelling Canadian men who have sex with men.

A small but consistent literature from the United States suggests increased risk for smoking among lesbians and men who have sex with men (MSM). Few studies have investigated smoking among MSM in other countries where different social norms and restrictions on smoking in public apply. We measured smoking behaviours in a convenience sample of urban-dwelling young Canadian MSM (median age 28 years). We compared the prevalence of smoking among MSM with that among other men in British Columbia (BC) using National Population Health Survey data to compute an age-adjusted standardized prevalence ratio (SPR). Independent predictors of smoking among MSM were identified using adjusted odds ratios (OR) with 95% confidence intervals (CI). Smoking during the previous year was reported by twice as many MSM (54.5% of 354) as other men in BC (25.9%) (SPR = 1.94, 95% CI 1.48-2.59), with largest differentials observed among men under 25 years of age. In multivariable analyses, smoking among MSM was significantly associated with younger age (OR 0.94, CI 0.88-1.00 per year), greater number of depressive symptoms (OR 1.12, CI 1.06-1.19 per symptom) and Canadian Aboriginal ethnicity (OR 2.64, CI 1.05-6.60). In summary, MSM in our study were twice as likely to smoke as other men in BC; the greatest differences were observed among the youngest men. The design of effective prevention and cessation programs for MSM will require identification of the age-dependent determinants of smoking initiation, persistence, and attempts to quit.